Judith, what I think you mean by public taxis are publicos, or public cars. They are just like the guaguas (the vans) in that they stop and pick up passengers along the road and have no fixed schedule. The normal load for a publico is 4 passengers in back seat and two in front with the driver.
The publicos that run between Puerto Plata and Sosua have a red box on the roof. The cars that go from Sosua to Cabarete and beyond have a blue box on the top. If you know the rate and give that to the driver at your destination, he will not ask for more. When you don't know the rate, you are vulnerable to being over charged. Knowing the language isn't what makes the difference, it is knowing what is the correct amount to pay the driver and to have the right amount of change.
With respect to fares, the publicos charge about RD$5 more than the guaguas, but they are worth it because you get where you are going faster and because it is not hectic like it can be on the guaguas with people crawling over you to get out and others crawling over you to get in.
I've been riding guaguas and publicos for more than 20 years.
The guaguas are almost always over crowded because the driver figures that no matter how full the guagua is there is room for more. This is not the case with the publicos. My wife and I always take the publicos for that reason and because you can pay for an extra seat. For example, when my wife goes to Puerto Plata she sits in the front seat and pays the driver for two fares. That way she is alone with the driver in the front and much more comfortable.